L ∞-Estimates of Rectangular Mixed Methods for Nonlinear Constrained Optimal Control Problem

In this paper, we investigate the rectangular mixed finite element methods for the quadratic convex optimal control problem governed by nonlinear elliptic equations with pointwise control constraints. The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive L ?-error estimates for the rectangular mixed finite element approximation of nonlinear quadratic optimal control problems. Finally, we present some numerical examples which confirm our theoretical results.